Advanced Solving Systems of Equations

The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?

• x=8

• x=3

• x=11

• x=5

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120

• 3x+3y=134
  4x+3y=120

• 4x+3y=134
  3x+3y=120

• 7xy=134
  6xy=120

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 

• 1

• -1

• 3

• 4

Write the inequalities represented in the picture.

• y ≤ 3x   and  y ≤ -2x + 4

• y > 3x   and  y > -2x + 4

• y < 3x   and  y > -2x + 4

• y > 3x   and  y < -2x + 4

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

Write the inequalities represented in the picture.

• y > -2 + x
  y ≤ 2x + 2

• y > 2 + x
  y ≤ 2x + 2

• y ≥ -2 + x
  y ≤ 2x + 2

• none of these are the system

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30

These two lines intersect at _____

• (4, -2)

• (4, 2)

• (-2, 4) 

• No solution